Crane jib attitude and heading reference system and method

ABSTRACT

Methods and apparatus are provided for determining the attitude and heading angle of a crane jib. Crane jib angular velocity, crane jib roll angle, crane jib pitch angle, crane jib specific force, and magnetic field in the local operating environment of the crane jib are all sensed and supplied to a processor. All of these measurements are processed, in a processor, to estimate the attitude and heading angle of the crane jib.

TECHNICAL FIELD

The present invention generally relates to an attitude and headingreference system, and more particularly relates to an attitude andheading reference system for the jib of a crane.

BACKGROUND

Tower cranes are used in myriad environments. Two of the more commonenvironments are construction sites and shipbuilding facilities, becauseof the combination of height and lifting capacity this type of craneprovides. A tower crane typically includes a base, a mast, and a cranejib. The base is fixed to the ground, and is also connected to the mast.A slewing unit is connected to the mast and is used to rotate the crane.The crane jib includes, among other things, a load-bearing section, acounter jib section, and the operator cab.

The load-bearing section of the crane jib typically carries a load. Thecounter jib section is connected to the load-bearing section, andcarries a counterweight to balance the crane jib while the load-bearingsection is carrying a load. The operator cab is usually located near thetop of the mast, and may be attached to the crane jib. However, othertower cranes may have the operator cab mounted partway down the mast. Nomatter its specific location, a crane operator sits in the operator caband controls the crane. In some instances, a crane operator can remotelycontrol one or more tower cranes from the ground.

In some environments, a plurality of tower cranes may be operated inrelatively close proximity. Thus, while it is unlikely, it has beenpostulated that the crane jibs of two or more tower cranes couldcollide. Hence, there is a need for a collision avoidance/warning systemthat is able to determine the three-dimensional (3D) angular orientation(e.g., attitude and heading angle) of a crane's own crane jib and ofother crane jibs working at a particular site. The present inventionaddresses at least this need.

BRIEF SUMMARY

In one embodiment, a method of determining the attitude and headingangle of a crane jib includes sensing crane jib angular velocity,sensing crane jib roll angle, sensing crane jib pitch angle, sensingspecific force acting on a portion of the crane jib, and sensing localmagnetic field at least proximate the crane jib. The sensed crane jibangular velocity, the sensed crane jib roll angle, the sensed crane jibpitch angle, the sensed specific force, and the sensed local magneticfield are all supplied to a processor. In the processor, crane jibtranslational velocity is computed from the sensed crane jib angularvelocity and the sensed specific force, and crane jib acceleration iscomputed using the computed crane jib translational velocity and thesensed crane jib angular velocity. The computed crane jib accelerationis used to remove crane jib acceleration components from the sensedcrane jib roll angle and the sensed crane jib pitch angle, and tothereby supply corrected crane jib roll angle measurements and correctedcrane jib pitch angle measurements. Calibration parameters are appliedto the sensed local magnetic field, to thereby supply calibratedmagnetic field measurements. Crane jib heading angle is computed fromthe calibrated magnetic field measurements. The corrected crane jib rollangle measurements, the corrected crane jib pitch angle measurements,and the computed crane jib heading angle, are used to estimate theattitude and heading angle of the crane jib.

In another embodiment, a crane jib attitude and heading reference systemincludes a plurality of crane jib angular velocity sensors, a pluralityof specific force sensors, an inclinometer, a plurality ofmagnetometers, and a processor. Each crane jib angular velocity sensoris configured to sense crane jib angular velocity and supply angularvelocity signals representative thereof. Each specific force sensor isconfigured to sense specific forces acting on the crane jib and supplyspecific force sensor signals representative thereof. The inclinometeris configured to sense crane jib roll angle and crane jib pitch angleand supply inclinometer signals representative thereof. Eachmagnetometer is configured to sense local magnetic field at leastproximate the crane jib and supply magnetometer signals representativethereof. The processor is coupled to receive the angular velocitysignals, the specific force sensor signals, the inclinometer signals,and the magnetometer signals and is configured, in response thereto, tocompute crane jib translational velocity from the sensed crane jibangular velocities and the sensed specific forces, compute crane jibacceleration using the computed crane jib translational velocity and thesensed crane jib angular velocities, use the computed crane jibacceleration to remove crane jib acceleration components from the sensedcrane jib roll angle and the sensed crane jib pitch angle, and tothereby supply corrected crane jib roll angle measurements and correctedcrane jib pitch angle measurements, apply calibration parameters to thesensed local magnetic fields, to thereby supply calibrated magneticfield measurements, compute crane jib heading angle from the calibratedmagnetic field measurements, and using the corrected crane jib rollangle measurements, the corrected crane jib pitch angle measurements,and the computed crane jib heading angle, to estimate the attitude andheading angle of the crane jib.

In yet another embodiment, a crane jib attitude and heading referencesystem includes a plurality of crane jib angular velocity sensors, aninclinometer, a plurality of accelerometers, a plurality ofmagnetometers, a display device, and a processor. Each crane jib angularvelocity sensor is configured to sense crane jib angular velocity andsupply angular velocity signals representative thereof. The inclinometeris configured to sense crane jib roll angle and crane jib pitch angleand supply inclinometer signals representative thereof. Eachaccelerometer is configured to sense forces acting on a proof mass andsupply specific force sensor signals representative thereof. Eachmagnetometer is configured to sense local magnetic field at leastproximate the crane jib and supply magnetometer signals representativethereof. The processor is coupled to the display device and furthercoupled to receive the angular velocity signals, the inclinometersignals, the specific force signals, and the magnetometer signals. Theprocessor is configured, upon receipt of the angular velocity signals,the inclinometer signals, the specific force signals, and themagnetometer signals, to compute corrected accelerometer measurementsusing the sensed forces acting on the proof mass, gravity, andpredictions of accelerometer bias, compute corrected angular velocitymeasurements using the sensed angular velocity and predictions ofangular velocity sensor bias, compute estimates of crane jibtranslational velocity using the corrected angular velocitymeasurements, compute corrected crane jib roll and pitch angles from theinclinometer signals and the estimates of crane jib translationalvelocity, compute crane jib heading angle from the magnetometer signals,implement a first filter that receives the computed estimates of cranejib velocity, computes predictions of crane jib velocity, and computesthe predictions of accelerometer bias, implement a second filter thatreceives the computations of corrected crane jib roll and pitch anglesand the computations of crane jib heading angle, computes thepredictions of angular velocity sensor bias, and determines crane jibattitude and heading angle, and supplies image rendering displaycommands to the display device that cause the display device to renderthe crane jib attitude and heading angle thereon.

Furthermore, other desirable features and characteristics of the cranejib attitude and heading system and method will become apparent from thesubsequent detailed description and the appended claims, taken inconjunction with the accompanying drawings and the preceding background.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will hereinafter be described in conjunction withthe following drawing figures, wherein like numerals denote likeelements, and wherein:

FIG. 1 depicts a side view of an embodiment of a tower crane;

FIG. 2 depicts a functional block diagram of a crane jib attitude andheading reference system (AHRS) that may be used in the tower crane ofFIG. 1;

FIG. 3 depicts a process, in flowchart form, that is implemented by thecrane jib AHRS of FIG. 2; and

FIG. 4 depicts the crane jib AHRS of FIG. 2 with various functionsimplemented within the processor, when carrying out the process of FIG.3, depicted in more detail.

DETAILED DESCRIPTION

The following detailed description is merely exemplary in nature and isnot intended to limit the invention or the application and uses of theinvention. As used herein, the word “exemplary” means “serving as anexample, instance, or illustration.” Thus, any embodiment describedherein as “exemplary” is not necessarily to be construed as preferred oradvantageous over other embodiments. All of the embodiments describedherein are exemplary embodiments provided to enable persons skilled inthe art to make or use the invention and not to limit the scope of theinvention which is defined by the claims. Furthermore, there is nointention to be bound by any expressed or implied theory presented inthe preceding technical field, background, brief summary, or thefollowing detailed description. In this regard, although the attitudeand heading reference system is described herein as being implementedwith a tower crane, it will be appreciated that it can be implementedwith other types of cranes, such as luffing cranes.

Referring first to FIG. 1, a side view of one embodiment of a towercrane 100 is depicted. The depicted crane 100 is a tower crane, thoughany one of numerous other types of cranes could also be used. Thedepicted crane 100 includes a base 102, a mast 104, and a slewing unit106. The base is affixed to a surface 108, such as the ground, and isused to support the remainder of the components that comprise the towercrane 100. The mast 104, which may be implemented as an adjustableheight mast, is coupled at one end to the base 102. The slewing unit 106is rotationally coupled to the opposing end of the mast 104, and isadditionally coupled to a crane jib structure 110, which includes aload-bearing section 112, a counter jib section 114, and an operator cab116. Before proceeding further, it is noted that when the term “cranejib” is used herein, it encompasses: the entire crane jib structure 110,the load-bearing section 112 and the counter jib section 114, just theload-bearing section 112, or just the counter jib section 114.

The load-bearing section 112, which in the depicted embodiment comprisesa plurality of lattice-structure elements, is coupled at one end to theslewing unit 106 and extends therefrom to a second end. A cable trolley118 may be mounted on the load-bearing section 112 and may becontrollably moved to a plurality of positions between the ends of theload-bearing section 112. The counter jib section 114 is coupled to theslewing unit 106 on a side opposite the load-bearing section 112, andhas a counter weight 122 coupled thereto. The operator cab 116 iscoupled to the slewing unit 106 and, at least in the depictedembodiment, is located under the load-bearing section 112.

An operator, disposed within the operator cab 116, controls the towercrane 100. In particular, an operator, via a plurality ofnon-illustrated motors and gear sets, may rotate the slewing unit 106,and thus the crane jib, relative to the mast 104, about a firstorthogonal axis 124. The dynamics of the crane jib during operation, aswell as the environmental conditions, may additionally cause the cranejib to rotate about a second orthogonal axis 126 (depicted as a dot torepresent an axis into and out of the plane of the paper), and a thirdorthogonal axis 128. As used herein, rotation about the first orthogonalaxis 124 varies the heading angle of the crane jib, rotation about thesecond orthogonal axis 126 varies the pitch angle of the crane jib, androtation about the third orthogonal axis 128 varies the roll angle ofthe crane jib.

The tower crane 100 may, in some instances, be operated in relativelyclose proximity with one or more other, non-illustrated tower cranes.Thus, to even further reduce the likelihood that the crane jib 110 willcollide with that of another tower crane, the depicted tower crane 100is additionally equipped with a crane jib attitude and heading referencesystem (AHRS). An exemplary embodiment of the crane jib AHRS 200 isdepicted in FIG. 2 and with reference thereto will now be described.

The depicted crane jib AHRS 200 includes a plurality of crane jibangular velocity sensors 202 (202-1, 202-2, 202-3), a plurality ofmagnetometers 204 (204-1, 204-2, 204-3), a plurality of accelerometers206 (206-1, 206-2, 206-3), an inclinometer 208, a processor 210, and adisplay device 212. The crane jib angular velocity sensors 202 are eachconfigured to sense the angular velocity of the crane jib, and supplyangular velocity signals representative thereof. The magnetometers 204are each configured to sense the local magnetic field at least proximatethe crane jib, and supply magnetometer signals representative thereof.More specifically, the magnetometers 204 provide a measurement of thelocal magnetic field vector resolved along the orientations of themeasurement axes. Because the magnetometers 204 are attached to thecrane jib 110, the magnetometers 204 and the crane jib 110 have a fixedrelative orientation. Hence, the orientation of the magnetometers 204 isdirectly correlative to that of the crane jib 110. The accelerometers206 are each configured to sense forces acting on a proof mass (notdepicted), and supply specific force signals representative thereof. Theinclinometer 208 is configured to sense the roll angle and the pitchangle of the crane jib, and supply inclinometer signals representativethereof.

It will be appreciated that the number and type of crane jib angularvelocity sensors 202, the number and type of magnetometers 204, and thenumber and type of accelerometers 206, may vary. In the depictedembodiment, however, the crane jib angular velocity sensors 202 areimplemented using three, orthogonally disposed rate gyroscopes(“gyros”), the magnetometers 204 are implemented using three,orthogonally disposed magnetometers, and the accelerometers 206 areimplemented using three, orthogonally disposed accelerometers. Althoughthe specific type of rate gyros 202, magnetometers 204, accelerometers206, and inclinometer 208 that are used may also vary, in one particularembodiment, an HG1171 Inertial Measurement Unit (IMU) manufactured byHoneywell International, Inc., and which includes all of these devicesin a single housing, is used. It will be appreciated that in otherembodiments, separately housed sensors may be used.

No matter the specific implementation of the crane jib angular velocitysensors 202, the magnetometers 204, the accelerometers 206, and theinclinometer 208, the processor 210 is coupled to receive the angularvelocity signals, the magnetometer signals, the specific force signals,and the inclinometer signals, respectively, therefrom. The processor 210is configured, in response to these signals to determine the attitudeand heading angle of the crane jib. The processor 210 additionallysupplies image rendering display commands to the display device 212. Theimage rendering display commands cause the display device 212 to renderthe determined crane jib attitude and heading angle thereon.

Before proceeding further, it should be noted that the display device212 may be implemented using any one of numerous known display devicessuitable for rendering image and/or text data in a format viewable by acrane operator. Non-limiting examples of such display devices includevarious cathode ray tube (CRT) displays, and various flat panel displayssuch as, various types of LCD (liquid crystal display) and TFT (thinfilm transistor) displays, just to name a few.

The processor 210 is configured to implement various functions in orderto determine the attitude and heading angle of the crane jib from theangular velocity signals, the magnetometer signals, the specific forcesignals, and the inclinometer signals. In particular, and as FIG. 2further depicts, the processor 210 implements two Kalman filters—a firstKalman filter 214 and a second Kalman filter 216. As will be describedin more detail below, the first Kalman filter 214, which is referred toherein as a velocity Kalman filter, computes predictions of the velocityof the crane jib, and predictions of accelerometer bias. The measurementvector for the velocity Kalman filter 214 is the velocity of the cranejib, which is computed from corrected angular velocity measurements. Thecomputed velocity of the crane jib 110 is also used to compute theacceleration of the crane jib 110, which is used to correct the rollangle and pitch angle sensed by the inclinometer. The second Kalmanfilter 216, which is referred to herein as the quaternion Kalman filter,computes predictions of angular velocity sensor bias, and determines theattitude and heading angle of the crane jib. The measurement vector forthe quaternion Kalman filter 216 comprises the above-mentioned correctedcrane jib roll and the pitch angles, and crane jib heading angle that isdetermined from the magnetometer signals. It should be noted that cranejib heading angle is the heading angle relative to the initial angularorientation of the crane jib.

As is generally known, a Kalman filter implements an iterative two-stepprediction-correction process to estimate a state vector. The predictionportion of this process is sometimes referred to as “the time update”because differential equations (e.g., a dynamic model) that govern thestate vector are propagated forward in time. The computationalresultants from the prediction portion of the process may be referred toas a priori estimates of the state vector. The correction portion ofthis process is sometimes referred to as “the measurement update”because a measurement vector is used to correct the a priori estimatesof the state vector that are computed in the prediction step. Thecomputational resultants from the correction portion of the process maybe referred to as posterior estimates of the state vector.

The crane jib AHRS 200, as was just noted, includes two Kalman filters214, 216. The two Kalman filters 214, 216 operate together. Thus, theoverall process implemented in processor 210 includes two predictionsteps and two correction steps. Moreover, the depicted Kalman filters214, 216 are configured such that a measurement vector drives theprediction steps and the correction steps. The overall process 300implemented in the processor 210 is depicted in flowchart form in FIG.3, and comprises the following iterative steps: predictions by thevelocity Kalman filter 214 (302), predictions by the quaternion Kalmanfilter 216 (304), corrections by the velocity Kalman filter 214 (306),various intermediate calculations (308), and corrections by thequaternion Kalman filter 304 (310). Because the process is iterative,these process steps are performed sequentially over and over again.

With reference now to FIG. 4, which depicts various functionsimplemented within the processor 210 in more detail, the processdepicted in FIG. 3 and described generally above will now be describedin more detail. The velocity Kalman filter prediction step (302) isperformed first. During this step, the velocity Kalman filter 214computes predictions of crane jib velocity 402, and predictions ofaccelerometer bias 404. These predictions are computed using a dynamicmodel 406, which is described in more detail below. The measurementsused to drive the velocity Kalman filter prediction step (302) arecompensated angular velocity measurements 424 and compensatedaccelerometer measurements 408. The compensated angular velocitymeasurements are the angular velocity signals supplied from the angularvelocity sensors 202 that have been compensated by the angular velocitysensor bias 420 (e.g., the posterior estimate from the previous timestep). The compensated accelerometer measurements 408 are accelerometersignals supplied from the accelerometers 206 that have been compensatedfor accelerometer bias 404 (e.g., the posterior estimate from theprevious time step) and gravity 412.

During the quaternion Kalman filter prediction step (304), thequaternion Kalman filter 216 computes predictions of crane jib 3Dangular orientation 414 (pitch angle, roll angle, and heading angle),and predictions of angular velocity sensor bias 420. These predictionsare also computed using a dynamic model 422, which is also described inmore detail below. The measurements used to drive the quaternion Kalmanfilter prediction step (304) are compensated angular velocitymeasurements 424.

The velocity Kalman filter correction step (306) is driven using acomputed crane jib velocity 426, which is supplied to a measurementmodel 407. The measurement model 407, like the dynamic model 406, willbe described further below. The crane jib velocity 426 that is suppliedto the measurement model 407 is computed from corrected angular velocitymeasurements 424 and the known position 428 (on the crane jib 110) ofthe angular velocity sensors 202. As was just noted, the correctedangular velocity measurements 424 are computed using the angularvelocity signals supplied from the angular velocity sensors 202 and theposterior estimates of the angular velocity sensor bias 420. It isadditionally noted that the predictions of crane jib velocity 402 andaccelerometer bias 404 that are computed after the velocity Kalmanfilter correction step (302) are the posterior estimates of crane jibvelocity 402 and accelerometer bias 404.

During the intermediate calculations step (308), several intermediatecalculations are performed. These calculations include computing cranejib acceleration 432 using the posterior estimate of crane jib velocity402 and the corrected crane jib angular velocity measurements 424(computed using the posterior estimate of angular velocity sensor bias420). Acceleration compensation 434 is applied to the inclinometersignals supplied from the inclinometer 208 using the computed crane jibacceleration 432. This compensation removes crane jib accelerationcomponents from the sensed crane jib roll angle and the sensed crane jibpitch angle, to thereby supply corrected crane jib roll anglemeasurements and corrected crane jib pitch angle measurements 436.Magnetometer calibration parameters 438 are applied to the magnetometersignals supplied from the magnetometers 204, to thereby generatecalibrated magnetometer measurements 416. The calibration parameters 438may be determined during an initial alignment procedure. The headingangle 442 of the crane jib 110 (relative to its initial angularorientation) is then calculated using the calibrated magnetometermeasurements 416. The corrected crane jib roll angle and pitch anglemeasurements 436 and the heading angle 442 are then converted toquaternions 444 and supplied to the quaternion Kalman filter 216. Itshould be noted that conversion to, and subsequent use of, quaternionsis just one technique that may be used to parameterize 3D angularorientation, and that numerous other attitude parameterization methodsmay be used. Some non-limiting examples include Euler angles, Rodriguesparameters, and direction cosines, just to name a few.

After the intermediate calculations step (308), the quaternion Kalmanfilter correction step (310) is performed. This step is driven using thecorrected roll angle and pitch angle 434 that are computed from theinclinometer signals, and the heading angle 442 computed from thecalibrated magnetometer measurements 438 (and that were converted toquaternions 444). These values are supplied to a measurement model 423,which will also be described further below. The posterior estimates ofcrane jib 3D angular orientation 414 (e.g., roll angle, pitch angle, andheading angle), and angular velocity sensor bias 420 are computed. Theposterior estimates of crane jib 3D angular orientation 414 are used togenerate image rendering display commands, which are supplied to thedisplay device 212. The display device 212, as previously noted, rendersan image of the crane jib attitude and heading angle.

It was noted in the discussion above that the dynamic models 406 and 422in the velocity Kalman filter 214 and the quaternion Kalman filter 216,respectively, would be described, as would the measurement models 407and 423 in the velocity Kalman filter 214 and the quaternion Kalmanfilter 216, respectively. For completeness, these descriptions will nowbe provided. Beginning first with the velocity Kalman filter 214, thedynamic model it implements is mathematically represented as follows:

$\begin{bmatrix}{\overset{\overset{.}{\_}}{v}}_{sensor} \\{\overset{\overset{.}{->}}{b}}_{f\; 1}\end{bmatrix} = {\begin{bmatrix}{- \left( {{\overset{->}{\omega}}_{m} - {\overset{\rightharpoonup}{b}}_{g} - {\overset{\rightharpoonup}{n}}_{g}} \right)^{x}} & {- I} \\0 & {{- \frac{1}{\tau_{a}}}I}\end{bmatrix}{\quad{{{\left\lbrack \frac{{\overset{\rightharpoonup}{v}}_{sensor}}{{\overset{\rightharpoonup}{b}}_{f\; 1}} \right\rbrack + {\left\lbrack \frac{I}{0} \right\rbrack\left( {{\overset{\rightharpoonup}{f}}_{m} - {\overset{\rightharpoonup}{b}}_{f\; 0} + {C_{bN}\overset{\rightharpoonup}{g}}} \right)} + {{\begin{bmatrix}{- I} & 0 \\0 & I\end{bmatrix}\left\lbrack \frac{{\overset{\rightharpoonup}{n}}_{f}}{{\overset{\rightharpoonup}{n}}_{f\; 1}} \right\rbrack}Q_{v,w}}} = {{diag}\begin{bmatrix}\sigma_{fx}^{2} & \sigma_{fy}^{2} & \sigma_{fz}^{2} & \frac{2\sigma_{f\; 1x}^{2}}{\tau_{a}} & \frac{2\sigma_{f\; 1y}^{2}}{\tau_{a}} & \frac{2\sigma_{f\; 1z}^{2}}{\tau_{a}}\end{bmatrix}}},}}}$

-   -   where {right arrow over (v)}_(sensor) is the velocity vector of        the sensor, {right arrow over (ω)}_(m) is the measured angular        velocity vector of the crane jib, {right arrow over (f)}_(m) the        measured specific force vector of the crane jib, {right arrow        over (g)} is the local gravity vector, {right arrow over        (b)}_(g) is the rate gyro bias vector, {right arrow over        (n)}_(g) is the rate gyro measurement noise vector, {right arrow        over (b)}_(f) is the accelerometer bias vector, {right arrow        over (b)}_(f0) is the accelerometer bias null shift vector,        {right arrow over (b)}_(f1) is the accelerometer bias drift rate        vector, {right arrow over (n)}_(f) is the accelerometer        measurement noise vector, {right arrow over (n)}_(f1) is the        accelerometer bias Gauss-Markov driving-process noise vector,        σ_(f) is the standard deviation of the accelerometer measurement        noise, σ_(f1) is the standard deviation of the accelerometer        bias Gauss-Markov driving-process noise, τ_(a) is the        correlation time of the accelerometer bias Gauss-Markov process,        Q_(v,w) is the power spectral density of the velocity Kalman        filter process noise vector defined by the accelerometer        measurement noise vector and the accelerometer bias Gauss-Markov        driving-process noise vector, and C_(bN), is the direction        cosine matrix from the crane jib navigation frame to the sensor        body frame.        And the measurement model implemented by the velocity Kalman        filter 214 is mathematically represented as follows:

${\left( {{\overset{\rightharpoonup}{\omega}}_{m} - {\overset{\rightharpoonup}{b}}_{g}} \right)^{x}{\overset{\rightharpoonup}{r}}_{sensor}} = {{\begin{bmatrix}I & 0\end{bmatrix}\left\lbrack \frac{{\overset{\rightharpoonup}{v}}_{sensor}}{{\overset{\rightharpoonup}{b}}_{f\; 1}} \right\rbrack} - {\left( {\overset{\rightharpoonup}{r}}_{sensor} \right)^{x}{\overset{\rightharpoonup}{n}}_{g}}}$${R_{v} = {{\left( {\overset{\rightharpoonup}{r}}_{sensor} \right)^{x}{diag}\left\lfloor \begin{matrix}\sigma_{gx}^{2} & \sigma_{gy}^{2} & \sigma_{gz}^{2}\end{matrix} \right\rfloor\left( {\overset{\rightharpoonup}{r}}_{sensor} \right)^{xT}} + {\left( {{1e} - 6} \right)I}}},$

-   -   where, in addition to those variables previously defined, {right        arrow over (r)}_(sensor) is the position vector of the sensor        relative to crane jib's center of rotation, σ_(g) is the        standard deviation of the rate gyro measurement noise, and R_(v)        is the covariance matrix of the crane jib angular velocity        computed from the compensated angular velocity measurements and        sensor position vector.

The dynamic model implemented in the quaternion Kalman filter 216 ismathematically represented as follows:

$\left\lbrack \frac{\delta{\overset{\overset{.}{\_}}{q}(t)}}{{\overset{\overset{.}{->}}{b}}_{g\; 1}(t)} \right\rbrack = {{\begin{bmatrix}{- \left( {{\overset{\rightharpoonup}{\omega}}_{m} - {\overset{\rightharpoonup}{b}}_{g}} \right)^{x}} & {{- \frac{1}{2}}I} \\0 & {{- \frac{1}{\tau_{g}}}I}\end{bmatrix}\left\lbrack \frac{\delta{\overset{\_}{q}(t)}}{{\overset{\_}{b}}_{g\; 1}(t)} \right\rbrack} + {\begin{bmatrix}{{- \frac{1}{2}}I} & 0 \\0 & I\end{bmatrix}\left\lbrack \frac{{\overset{\rightharpoonup}{n}}_{g}(t)}{{\overset{\rightharpoonup}{n}}_{g\; 1}(t)} \right\rbrack}}$${Q_{q,w} = {{diag}\begin{bmatrix}\sigma_{gx}^{2} & \sigma_{gy}^{2} & \sigma_{gz}^{2} & \frac{2\sigma_{g\; 1x}^{2}}{\tau_{g}} & \frac{2\sigma_{g\; 1y}^{2}}{\tau_{g}} & \frac{2\sigma_{g\; 1z}^{2}}{\tau_{g}}\end{bmatrix}}},$

-   -   where, in addition to those variables previously defined,        δ{right arrow over (q)} is the vector error component of the        estimated quaternion, {right arrow over (b)}_(g0) is the rate        gyro bias null shift vector, {right arrow over (b)}_(g1) is the        rate gyro bias drift rate vector, {right arrow over (n)}_(g1) is        the rate gyro bias Gauss-Markov driving-process noise vector,        σ_(g1) is the standard deviation of the rate gyro bias Gauss        Markov driving-process noise, τ_(g) is the correlation time of        the rate gyro bias Gauss Markov process, and Q_(q,w) is the        power spectral density of the quaternion Kalman filter process        noise vector defined by the rate gyro measurement noise vector        and the rate gyro bias Gauss-Markov driving-process noise        vector.        And the measurement model implemented by the quaternion Kalman        filter 216 is mathematically represented as follows:

${{{- q_{4}}\overset{\hat{\_}}{q}} + {{\overset{\_}{q}}^{x}\overset{\hat{\_}}{q}} + {{\hat{q}}_{4}\overset{\_}{q}}} = {\begin{bmatrix}I & 0\end{bmatrix}\left\lbrack \frac{\delta{\overset{\_}{q}(t)}}{{\overset{->}{b}}_{g\; 1}(t)} \right\rbrack}$${R_{q} = {{diag}\begin{bmatrix}\left\lbrack \frac{\sigma_{{inc},x}}{2} \right\rbrack^{2} & \left\lbrack \frac{\sigma_{{inc},y}}{2} \right\rbrack^{2} & \left\lbrack \frac{\sigma_{mag}}{2} \right\rbrack^{2}\end{bmatrix}}},$

-   -   where, in addition to those variables previously defined, {right        arrow over ({circumflex over (q)} is the vector component of the        estimated quaternion, {circumflex over (q)}₄ is the scalar        component of the estimated quaternion, {right arrow over (q)} is        the vector component of the quaternion computed from the        corrected roll angle and pitch angle 434 that are computed from        the inclinometer signals, and the relative heading angle 442        computed from the calibrated magnetometer measurements 438, q₄        is the scalar component of the quaternion computed from the        corrected roll angle and pitch angle 434 that are computed from        the inclinometer signals, and the relative heading angle 442        computed from the calibrated magnetometer measurements 438,        σ_(inc,x) is the standard deviation of the roll angle        inclinometer measurement, σ_(inc,y) is the standard deviation of        the pitch angle inclinometer measurement, σ_(mag) is the        standard deviation of the heading angle measurement computed        from the calibrated magnetometer measurements 438, and R_(q) is        the covariance matrix of the crane jib attitude and heading        angle measurements computed from the corrected roll angle and        pitch angle 434 that are computed from the inclinometer signals,        and the relative heading angle 442 computed from the calibrated        magnetometer measurements 438.

The crane jib attitude and heading reference system and method disclosedherein may be used to determine the attitude and heading angle of acrane jib. If the disclosed system is installed in other cranes, thesame information may be provided from other crane jibs working at aparticular site. The crane jib attitude and heading reference systemdiffers from other attitude and heading reference systems in that itimplements a two-stage Kalman filter (e.g., velocity Kalman filter 214and quaternion Kalman filter 216) to estimate crane jib attitude andheading angle, crane jib velocity is estimated to remove accelerationcomponents from the accelerometer measurements thereby correctinginclinometer measurements, and measurements of crane jib velocity arebased on the dynamics of the crane jib.

Those of skill in the art will appreciate that the various illustrativelogical blocks, modules, circuits, and algorithm steps described inconnection with the embodiments disclosed herein may be implemented aselectronic hardware, computer software, or combinations of both. Some ofthe embodiments and implementations are described above in terms offunctional and/or logical block components (or modules) and variousprocessing steps. However, it should be appreciated that such blockcomponents (or modules) may be realized by any number of hardware,software, and/or firmware components configured to perform the specifiedfunctions. To clearly illustrate this interchangeability of hardware andsoftware, various illustrative components, blocks, modules, circuits,and steps have been described above generally in terms of theirfunctionality. Whether such functionality is implemented as hardware orsoftware depends upon the particular application and design constraintsimposed on the overall system. Skilled artisans may implement thedescribed functionality in varying ways for each particular application,but such implementation decisions should not be interpreted as causing adeparture from the scope of the present invention. For example, anembodiment of a system or a component may employ various integratedcircuit components, e.g., memory elements, digital signal processingelements, logic elements, look-up tables, or the like, which may carryout a variety of functions under the control of one or moremicroprocessors or other control devices. In addition, those skilled inthe art will appreciate that embodiments described herein are merelyexemplary implementations.

The various illustrative logical blocks, modules, and circuits describedin connection with the embodiments disclosed herein may be implementedor performed with a general purpose processor, a digital signalprocessor (DSP), an application specific integrated circuit (ASIC), afield programmable gate array (FPGA) or other programmable logic device,discrete gate or transistor logic, discrete hardware components, or anycombination thereof designed to perform the functions described herein.A general-purpose processor may be a microprocessor, but in thealternative, the processor may be any conventional processor,controller, microcontroller, or state machine. A processor may also beimplemented as a combination of computing devices, e.g., a combinationof a DSP and a microprocessor, a plurality of microprocessors, one ormore microprocessors in conjunction with a DSP core, or any other suchconfiguration. The word “exemplary” is used exclusively herein to mean“serving as an example, instance, or illustration.” Any embodimentdescribed herein as “exemplary” is not necessarily to be construed aspreferred or advantageous over other embodiments.

The steps of a method or algorithm described in connection with theembodiments disclosed herein may be embodied directly in hardware, in asoftware module executed by a processor, or in a combination of the two.A software module may reside in RAM memory, flash memory, ROM memory,EPROM memory, EEPROM memory, registers, hard disk, a removable disk, aCD-ROM, or any other form of storage medium known in the art. Anexemplary storage medium is coupled to the processor such the processorcan read information from, and write information to, the storage medium.In the alternative, the storage medium may be integral to the processor.The processor and the storage medium may reside in an ASIC. The ASIC mayreside in a user terminal In the alternative, the processor and thestorage medium may reside as discrete components in a user terminal.

In this document, relational terms such as first and second, and thelike may be used solely to distinguish one entity or action from anotherentity or action without necessarily requiring or implying any actualsuch relationship or order between such entities or actions. Numericalordinals such as “first,” “second,” “third,” etc. simply denotedifferent singles of a plurality and do not imply any order or sequenceunless specifically defined by the claim language. The sequence of thetext in any of the claims does not imply that process steps must beperformed in a temporal or logical order according to such sequenceunless it is specifically defined by the language of the claim. Theprocess steps may be interchanged in any order without departing fromthe scope of the invention as long as such an interchange does notcontradict the claim language and is not logically nonsensical.

Furthermore, depending on the context, words such as “connect” or“coupled to” used in describing a relationship between differentelements do not imply that a direct physical connection must be madebetween these elements. For example, two elements may be connected toeach other physically, electronically, logically, or in any othermanner, through one or more additional elements.

While at least one exemplary embodiment has been presented in theforegoing detailed description of the invention, it should beappreciated that a vast number of variations exist. It should also beappreciated that the exemplary embodiment or exemplary embodiments areonly examples, and are not intended to limit the scope, applicability,or configuration of the invention in any way. Rather, the foregoingdetailed description will provide those skilled in the art with aconvenient road map for implementing an exemplary embodiment of theinvention. It being understood that various changes may be made in thefunction and arrangement of elements described in an exemplaryembodiment without departing from the scope of the invention as setforth in the appended claims.

What is claimed is:
 1. A method of determining the attitude and headingangle of a crane jib, comprising the steps of: sensing crane jib angularvelocity; sensing crane jib roll angle; sensing crane jib pitch angle;sensing specific force acting on a portion of the crane jib; sensinglocal magnetic field at least proximate the crane jib; supplying thesensed crane jib angular velocity, the sensed crane jib roll angle, thesensed crane jib pitch angle, the sensed specific force, and the sensedlocal magnetic field to a processor; and in the processor: computingcrane jib translational velocity from the sensed crane jib angularvelocity and the sensed specific force; computing crane jib accelerationusing the computed crane jib translational velocity and the sensed cranejib angular velocity; using the computed crane jib acceleration toremove crane jib acceleration components from the sensed crane jib rollangle and the sensed crane jib pitch angle, and to thereby supplycorrected crane jib roll angle measurements and corrected crane jibpitch angle measurements; applying calibration parameters to the sensedlocal magnetic field, to thereby supply calibrated magnetic fieldmeasurements; computing crane jib heading angle from the calibratedmagnetic field measurements; and using the corrected crane jib rollangle measurements, the corrected crane jib pitch angle measurements,and the computed crane jib heading angle, to estimate the attitude andheading angle of the crane jib.
 2. The method of claim 1, furthercomprising: computing a crane jib angular velocity sensor bias;computing corrected crane jib angular velocity measurements from thesensed crane jib angular velocity and the crane jib angular velocitysensor bias.
 3. The method of claim 2, wherein crane jib velocity iscalculated using the corrected crane jib angular velocity measurements.4. The method of claim 2, wherein: crane jib angular velocity is sensedusing three orthogonally disposed rate gyros; the rate gyros are eachlocated at a position on the crane jib; and crane jib velocity iscomputed using the corrected crane jib angular velocity measurements andthe position of each of the rate gyros.
 5. The method of claim 1,further comprising: in the processor: computing bias corrections; andcompensating the sensed specific force using the bias corrections andgravity, to thereby supply compensated specific force measurements. 6.The method of claim 5, wherein: the specific force acting on the cranejib is sensed using three orthogonally disposed accelerometers to sensethe sum of forces acting on a proof mass; and the step of computing thebias corrections comprises computing accelerometer bias corrections. 7.The method of claim 1, further comprising: converting each of thecorrected crane jib roll angle measurements, the corrected crane jibpitch angle measurements, and the computed crane jib heading angle to anattitude parameterization; and estimating the attitude and heading angleof the crane jib using the attitude parameterization.
 8. The method ofclaim 1, wherein roll angle and pitch angle are both sensed using one ormore of an inclinometer and an accelerometer.
 9. The method of claim 1,wherein the local magnetic field at least proximate the crane jib issensed using three orthogonally disposed magnetometers.
 10. The methodof claim 1, further comprising rendering the attitude and heading angleof the crane jib on a display device.
 11. A crane jib attitude andheading reference system, comprising: a plurality of crane jib angularvelocity sensors, each crane jib angular velocity sensor configured tosense crane jib angular velocity and supply angular velocity signalsrepresentative thereof; a plurality of specific force sensors configuredto sense specific forces acting on the crane jib and supply specificforce sensor signals representative thereof; an inclinometer configuredto sense crane jib roll angle and crane jib pitch angle and supplyinclinometer signals representative thereof; a plurality ofmagnetometers, each magnetometer configured to sense local magneticfield at least proximate the crane jib and supply magnetometer signalsrepresentative thereof; and a processor coupled to receive the angularvelocity signals, the specific force sensor signals, the inclinometersignals, and the magnetometer signals and configured, in responsethereto, to: compute crane jib translational velocity from the sensedcrane jib angular velocities and the sensed specific forces; computecrane jib acceleration using the computed crane jib translationalvelocity and the sensed crane jib angular velocities; use the computedcrane jib acceleration to remove crane jib acceleration components fromthe sensed crane jib roll angle and the sensed crane jib pitch angle,and to thereby supply corrected crane jib roll angle measurements andcorrected crane jib pitch angle measurements; apply calibrationparameters to the sensed local magnetic fields, to thereby supplycalibrated magnetic field measurements; compute crane jib heading anglefrom the calibrated magnetic field measurements; and using the correctedcrane jib roll angle measurements, the corrected crane jib pitch anglemeasurements, and the computed crane jib heading angle, to estimate theattitude and heading angle of the crane jib.
 12. The system of claim 11,further comprising: a display device coupled to the processor, thedisplay device configured to render thereon the attitude and headingangle of the crane jib.
 13. The system of claim 11, wherein theprocessor is further configured to: compute a crane jib angular velocitysensor bias correction; and compute corrected crane jib angular velocitymeasurements from the sensed crane jib angular velocities and the cranejib angular velocity sensor bias correction.
 14. The system of claim 12,wherein the processor calculates crane jib velocity using the correctedcrane jib angular velocity measurements.
 15. The system of claim 12,wherein: the plurality of crane jib angular velocity sensors comprisesthree orthogonally disposed rate gyros, each rate gyro located at aposition on the crane jib; and the processor computes crane jib velocityusing the corrected crane jib angular velocity measurements and theposition of each of the rate gyros.
 16. The system of claim 11, whereinthe processor is further configured, in response to the specific forcesensor signals to: compute bias corrections, and compensate the sensedspecific forces using the bias corrections and gravity, to therebysupply compensated specific force measurements.
 17. The system of claim16, wherein: the specific force sensors comprise three orthogonallydisposed accelerometers configured to sense the sum of forces acting ona proof mass; and the bias corrections comprise accelerometer biascorrections.
 18. The system of claim 11, wherein the processor isfurther configured to: convert each of the corrected crane jib rollangle measurements, the corrected crane jib pitch angle measurements,and the computed crane jib heading angle to quaternions; and estimatethe attitude and heading angle of the crane jib using the quaternions.19. The system of claim 11, wherein the plurality of magnetometerscomprises three orthogonally disposed magnetometers.
 20. A crane jibattitude and heading reference system, comprising: a plurality of cranejib angular velocity sensors, each crane jib angular velocity sensorconfigured to sense crane jib angular velocity and supply angularvelocity signals representative thereof; an inclinometer configured tosense crane jib roll angle and crane jib pitch angle and supplyinclinometer signals representative thereof; a plurality ofaccelerometers, each accelerometer configured to sense forces acting ona proof mass and supply specific force sensor signals representativethereof; a plurality of magnetometers, each magnetometer configured tosense local magnetic field at least proximate the crane jib and supplymagnetometer signals representative thereof; a display device; and aprocessor coupled to the display device and further coupled to receivethe angular velocity signals, the inclinometer signals, the specificforce signals, and the magnetometer signals, the processor configured,upon receipt of the angular velocity signals, the inclinometer signals,specific force signals, and the magnetometer signals, to: computecorrected accelerometer measurements using the sensed forces acting onthe proof mass, gravity, and predictions of accelerometer bias; computecorrected angular velocity measurements using the sensed angularvelocity and predictions of angular velocity sensor bias; computeestimates of crane jib translational velocity using the correctedangular velocity measurements and compensated accelerometermeasurements; compute corrected crane jib roll and pitch angles from theinclinometer signals and the estimates of crane jib translationalvelocity; compute crane jib heading angle from the magnetometer signals;implement a first filter that receives the computed estimates of cranejib velocity, computes predictions of crane jib velocity, and computesthe predictions of accelerometer bias; implement a second filter thatreceives the computations of corrected crane jib roll and pitch anglesand the computations of crane jib heading angle, computes thepredictions of angular velocity sensor bias, and determines crane jibattitude and heading angle; and supply image rendering display commandsto the display device that cause the display device to render the cranejib attitude and heading angle thereon.